For higher numbers of supersymmetries on the sigma model's world sheet, the target space dimension becomes negative. (Proof is a boring computation.) It's not particularly clear how to interpret this -- e.g., should the theory have a supergravity limit? -- so these theories are typically discarded from the classifications.
This post imported from StackExchange Physics at 2014-03-09 16:21 (UCT), posted by SE-user user1504